It concluded on Thursday that former home affairs minister Nkosazana Dlamini-Zuma unreasonably delayed the decision.
The appeal on the matter was brought by Inkatha Freedom Party leader Mangosuthu Buthelezi and Congress of the People leader Mosiuoa Lekota.
Earlier, the Western Cape High Court dismissed with costs an application on whether it had been constitutional for the government not to grant a visa to the Dalai Lama.
The Tibetan spiritual leader cancelled a trip to South Africa to attend Anglican Archbishop Emeritus Desmond Tutu's 80th birthday on October 4, last year.
Tutu was outraged and accused the current government of being worse than the apartheid-era one.
At the time, the high court found the issue was moot because the Dalai Lama, after getting no response to his visa application, cancelled his trip.
On Thursday, the appeal was upheld with costs.
His Holiness the 14th Dalai Lama, Tenzin Gyatso, is both the head of state and the spiritual leader of Tibet.
He has won many awards, including the Nobel Peace Prize, for promoting the cause of Tibet, and is welcome everywhere, except in South Africa and China. China invaded Tibet in 1950 and has occupied it since.
The Dalai Lama is a long-time friend of former president Nelson Mandela, Tutu, IFP leader Mangosuthu Buthelezi and former president FW De Klerk, who was the last president of the country in the apartheid era. – Sapa